Problem: Let $m=6x+5$. Which equation is equivalent to $(6x+5)^2-10=-18x-15$ in terms of $m$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $m^2+3m+5=0$ (Choice B) B $m^2-3m-10=0$ (Choice C) C $m^2-3m+5=0$ (Choice D) D $m^2+3m-10=0$
Solution: We are asked to rewrite the equation in terms of $m$, where ${m}={6x+5}$. In order to do this, we need to find all of the places where the expression ${6x+5}$ shows up in the equation, and then substitute ${m}$ wherever we see them! For instance, note that $-18x-15=-3({6x+5})$. This means that we can rewrite the equation as: $(6x+5)^2-10=-18x-15$ $({6x+5})^2-10=-3({6x+5})$ [What if I don't see this factorization?] Now we can substitute ${m}={6x+5}$ : $({m})^2-10=-3({m})$ Finally, let's manipulate this expression so that it shares the same form as the answer choices: ${m}^2+3{m}-10=0$ In conclusion, $m^2+3m-10=0$ is equivalent to the given equation when $m=6x+5$.